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A horizontal wire AB of length 'l' and m...

A horizontal wire AB of length 'l' and mass 'm' carries a steady current `I_1`, free to move in vertical plane is in equilibrium at a heigh of 'h' over another parallel long wire CD carrying a steady current `I_2`, which is fixed in a horizontal plane as shown. Derive the expression for the force acting per unit length on the wire AB and write the condition for which wire AB is in equilibrium.

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A long horizontal wire AB, which is free to move in a vertical plane and carries a steady current of 20 A, is in equilibrium at a height of 0.01 m over another parallel long wire CD which is fixed in a horizontal plane and carries a steady current of 30 A, as shown in figure. Shown that when AB is slightly depressed, it executes simple harmonic motion. Find the period of oscillations.